Higher Category Theory

Monday 14-16 and Friday 14-16, via zoom. Exercise class via GRIPS.

Higher Category Theory is the modern approach of Category Theory which includes the contribution of homotopy theory right from the start. This means that the way we identify objects and operators is much more general than equality or isomorphisms. This provides very powerful tools in algebraic topology and in algebraic geometry as well as in more applied areas such as computer science. This lecture, which will continue in the Summer Semester 2021 as well, aims at giving a proper introduction starting from scratch. In particular, no prior knowledge of category theory or of homotopy theory will be needed, and we will carefully state all definitions and give many examples. However, it is strongly recommended to follow a lecture on a related subject, such as Algebraic Topology 1 and/or Cohomology of sheaves 1 in order to build a good supply of non-trivial examples and of beautiful areas of mathematics where to apply the methods of Higher Category Theory.

Lecture notes.

Exercise Sheets